Bartlett et al. [1]} study the VC dimension for deep neural networks with piecewise linear activation functions (e.g., ReLU). Given a deep neural network with \(L\)  layers and \(W\)  parameters, they prove that the lower bound for VC dimension of such networks is \(\Omega (WL\log (W/L))\)  and the upper bound for VC dimension is \(O(WL\log W)\) .
